A Practical Guide to the Use of Major Elements, Trace Elements, and Isotopes in Compositional Data Analysis: Applications for Deep Formation Brine Geochemistry

Abstract

In the geosciences, isotopic ratios and trace element concentrations are often used along with major element concentrations to help determine sources of and processes affecting geochemical variation. Compositional Data Analysis (CoDA) is a set of tools, generally attuned to major element data, concerned with the proper statistical treatment and removal of spurious correlations from compositional data. Though recent insights have been made on the incorporation of trace elements and stable isotope ratios to CoDA, this study provides a general approach to thinking about how radiogenic isotopes, stable isotopes, and trace elements fit with major elements in the CoDA framework. In the present study, we use multiple data sets of deep formation brines and compare traditional mixing models to their CoDA counterparts to examine fluid movement between reservoirs. Concentrations of individual isotopes are calculated using isotopic ratios and global mean isotopic abundances. One key result is that isotope parts (e.g. $^{18}$O, $^{17}$O, $^{16}$O, $^{2}$H, $^{1}$H, $^{87}$Sr, $^{86}$Sr) can simply be modelled by the major element concentration (H$_{2}$O, Sr) in a clr-biplot as they are perfectly dependent. Another important result is that an ilr transformation of radiogenic isotope parts (e.g. $^{86}$Sr and $^{87}$Sr in $^{87}$Sr/$^{86}$Sr) and trace elements can, like stable isotopes in delta notation, be treated as a linear function of the isotopic ratio or trace element concentration, scaled only by a constant. This implies that there are multiple situations in which an ilr transformation provides little additional insight for the analysis of trends: (1) any two parts with low log ratio variance (e.g. an isotope ratio), no matter their concentrations in the solution, (2) any low concentration parts (trace elements) or a ratio of a trace to a major element, no matter the variance of the elements, and (3) large positive ratios (major/trace) over a restricted range of variance. Similarly, a multivariate ilr transformation of a large data set with many parts will also be a simple perturbation if the balances are evenly split between parts. CoDA transformations, however, even if they do not provide new insight in some specific cases, will provide consistent interpretations for all types of data.